4. This problem deals with a very practical
question that concerns the inhabitants of this
planet. The question is "in a democracy, when
can we expect the majority of citizens to favor
a government that provides private goods in a
public way?". This problem also addresses
issues of efficiency arising from the public
provision of private goods.
On planet Jumpo, there are two goods,
aerobics lessons and bread. The citizens all
have a Cobb-Douglas utility function of the
form Ui(Ai, Pi) = A₁ P₁" where Ai and Pi
are citizen i's consumption of aerobics and
bread.
Although tastes are all the same, there are two
different income groups, the rich and the poor.
Every rich person on Jumpo has an income of
100 fondas and every poor person has an
income of 50 fondas (fonda is the currency of
planet Jumpo). There are two million poor
people and one million rich. Bread is sold in the
usual way and costs 1 fonda. Aerobics lessons
are provided by the state, in identical
quantities for each person, and the price to the
state for aerobics lessons is 2 fondas per/nlesson. The cost of state-provided lessons is
paid for by taxes collected from citizens. The
state has no other expenses, so the sum of the
taxes must equal the total cost of the aerobics
lessons. Jumpo is a democracy, and the
number of aerobics lessons to be provided is
decided by a vote of the citizens.
a. Assume that the cost of state-provided
aerobics lessons is paid for by requiring each
person to pay an equal amount of taxes (per
capita taxation). If each citizen receives 20
lessons, what will be the government's total
expenditure on lessons? How many taxes will
each citizen have to pay? If 20 lessons are
given, how much will a rich person have left to
eat bread after paying the tax? What about a
poor person?
b. Since aerobics lessons are provided
publicly, everyone receives the same amount,
and no one can have more lessons for that
matter, each person faces the same
optimization problem. Write down this
optimization program and explain it.
c. How many lessons will the rich want the
state to provide? How many lessons will the
poor want the state to provide? (Still assuming
per capita taxation and identical quantities for
each individual).
d. If the result is determined by a majority vote,
how many aerobics lessons will be provided?/nhow many aerobics lessons will be provided?
How many loaves of bread will the rich get?
How many loaves of bread will the poor get?
e. Assume that aerobics lessons are
"privatized" in such a way that no lessons are
provided publicly and no taxes are collected.
Each person can buy as many lessons as they
like and as many loaves of bread as they like.
Assume that the price of the bread remains 1
fonda per unit and the price of the lesson
remains 2 fondas per unit. How many aerobics
lessons will the rich receive? And the poor?
How many loaves of bread will the rich buy?
And the poor?
f. Suppose that aerobics lessons remain
publicly available, but are paid for by a tax
proportional to income. Suppose that if A
aerobics lessons are offered to every person in
Jumpo, the tax for the rich will be 3A fondas
and the tax for the poor will be 1.5A fondas.
With these tax rates, how many aerobics
lessons will the rich get? And the poor? How
many aerobics lessons per head will the
majority vote for? How many loaves of bread
will the rich get? (Hint: remember to rewrite
each group's budget constraint)./ng. Calculate the utility of a rich person and a
poor person
i. If we apply a per capita tax
ii. In case of privatization
iii. If a tax proportional to income is applied
h. Compare these three systems according to
the Pareto criterion. Is privatization
Pareto superior to the per capita tax? Is the tax
proportional to income superior to the per
capita tax in the Pareto sense? Is privatization
superior in a Pareto sense to a tax proportional
to income? Explain your answers.
Fig: 1
Fig: 2
Fig: 3
Fig: 4
Most Viewed Questions Of Microeconomics
[1] What are the "choice variables and what are the "parameters' in this problem? What is the difference between them? [2] How do we know this problem has a solution? [3] Explain the relevant Lagrangian function. [4] Explain the conditions that will characterize a KT-point. [5] Use the conditions in part [4] to find the optimal consumption bundle (r*, y), and the associated Lagrange multiplier X*. [6] Explain why z* and y* can be interpreted as "functions". [7] Find the partial derivative of z* with respect to each "parameter of the problem". [8] Explain the interpretation of each partial derivate you find in part [7]. [9] Find the "indirect utility function' V = u(x, y), and explain its interpretation. [10] Find the partial derivative of V with respect to M, and explain its interpretation.
12) In the market for smartphones, the price elasticity of supply is +0.8, and the price elasticity of demand is -1.2. At equilibrium, price is $800 and quantity is 400000. (a) Assuming supply and demand are linear, reconstruct and draw the supply and demand curves. Label the intercepts. (b)To help consumers and phone-makers, the government proposes to subsidize smartphones by $80each. What are PB and PS after the subsidy? What is the new equilibrium quantity? Illustrate them on the same graph. (c) Calculate the change in consumer surplus, producer surplus, government expenditure, and dead weight loss and identify them on the graph.
7) Suppose that a consumer's marginal rate of substitution at her current chosen bundle is MUX /MUY = 4, but she is able to exchange X and Y at Px/PY = 3. Should she keep her current bundle,or can she make herself better off by trading at these prices? Which good will she buy, and which will she sell?
Question One Jane and John are a new couple trying to make a future production plan together. Assume there exist two types of production they can conduct: Household Production (HP) and Market Production (MP). If Jane does household production, her production value is $20 per hour; if she does market production, her production value is $10 per hour. If John does household production, his production value is $10 per hour; if he does market production, his production value is $20 per hour. Both Jane and John can work 8 hours on workdays. a) Calculate Jane and John's possible production frontiers (PPFs) on a workday and draw them in two diagrams. b) Combine Jane and John's PPFs in the same diagram. If both of them conduct market production, only, what would be their combined PPF? Show it in the diagram. If they do wish to keep some household production, who should do it? Show this new PPF in the diagram. Is there a limitation on this new PPF? c) On the other hand, if both Jane and John conduct household production, only, what would be their combined PPF? Show it in a diagram. If they do wish to keep some market production, who should do it? Show this new PPF in the diagram. Is there a limitation on this new PPF? d) If Jane and John "pool" their production possibilities together and split these possibilities equally between household production and market production, what would be their new PPFs? Show them in a diagram. e) Is there a gain for Jane and John to collaborate? If so, show it in a diagram.
5. (6 points) Suppose when we look at the monthly sales of hamburgers & fries in the Devil's Den, we see that when CCSU increased the price from $7 to $13, the quantity demanded fell from 8,000 meals to 4,000 meals.
QUESTION 4 A firm uses two inputs x and y, and their profit function is P(x,y)=3xy-2x+y. Input x costs $2 each and y costs $1 each and they are constrained to spend a total of $100 on inputs.
2. For each of the explanatory variables, P, CP, M and PE, calculate the respective demand elasticities for Hind Oil Industries’ product in the month September 2015. Remember to show all calculations. What additional information about Maa mustard oil do these values provide?
1. Analyze the estimated demand function by using the estimated coefficients to discuss the impact of each of the explanatory variables, P, CP, M, and PE, on the quantity of Maa mustard oil demanded. In discussing the impact, consider a one unit change in each variable while holding the others constant.
3) Illustrate the following utility functions by sketching indifference curves in the X,Y space: (Need not be to scale as long as the general shape is reasonable) (a) U(X,Y) = 2X + 3Y (perfect substitutes)(b) U(X,Y) = X1/2Y 1/2 (Cobb-Douglas) (c) Derive the expression for the Marginal Rate of Substitution for the utility functions above.
Two MSU fraternities, Phi Kappa Sigma and Phi Kappa Tau, are accustomed to each having 6 parties a month. Phi Kappa Sigma and Phi Kappa Tau are located close to each other on Bogue Street. These parties impose a negative externality on their other neighbors on Bogue Street. Suppose President Stanley decides that the socially optimal total number of parties on Bogue Street is 8 parties a month. The total benefits each fraternity derives from having a certain number of parties a month are given in the table below.
